In the Long Term Evolution (LTE) system, the random access technology is an important technology of accessing and controlling the user equipment in the communication system, and the receiver finishes uplink timing synchronous correction, user power adjustment and user resource requirement application through a random access process.
The cyclic shift sequence used by the uplink random access preamble of the LTE is the ZC (Zadoff-Chu) sequence, and the random access preamble code is derived by selecting different cyclic shifts based on the ZC sequence. The random access subframe is made up of three parts, respectively a Cyclic Prefix (CP), a random access preamble sequence and a Guard Time (GT), as shown in FIG. 1.
According to the difference of the cell coverage, the required CP lengths are different, and the preambles and the GT lengths are also different. The LTE system supports five formats, including Formats 0-4 respectively, and each format corresponds to a distinct cell coverage. The cell coverage radius is determined by the cyclic shift of the sequence and the GT together.
First of all, the cyclic shift determines whether the cell edge user is able to distinguish different cyclic shift windows, and the selection of the cyclic shift must guarantee that the relevant peak values of the local sequence and the preamble sequence of the cell edge user fall in the time window corresponding to the cyclic shift, and the length of the window is TNcs;
      T    Ncs    =            Ncs      Nzc        ×          T      SEQ        ×                  0.01        ⁢        s                    307200        ⁢        Ts            
Wherein, Nzc is the length of the ZC sequence; as to Formats 0-3, the value of the Nzc is 839; as to Format 4, the value of the Nzc is 139. TSEQ is the number of sampling points of the RACH preamble sequence.
The cell coverage radius determined by the Ncs can be obtained by the following formula,CellRadius1=0.5×TNcs×3×105 km/s
Because the time reference which reaches the receiver has a D1 time delay already after the downlink synchronization is finished, and there is also a D2 time delay after the receiver sends physical random access channel (PRACH) subframe to the base station, wherein, D=D1≈D2; therefore the time window TNcs corresponding to one cyclic shift needs to absorb two time delays 2D, so the supported cell radius should be reduced by half.
In addition, the cell radius relates to the GT as well, and the lengths of the CP and the GT determine that the random access channel (RACH) subframe of the cell edge user will not disturb the following subframes. There is also the problem of the uplink and downlink time delays 2D, and its calculation formula is as follows:
      CellRadius    ⁢                  ⁢    2    =      0.5    ×    GTnum    ×                  0.01        ⁢        s                    307200        ⁢                                  ⁢        Ts              ×    3    ×          10      5        ⁢                  ⁢    km    ⁢          /        ⁢    s  
Wherein, GTnum is the number of the sampling points in the guide time.
To sum up, the cell radius is determined by the lengths of the Ncs and the GT together:CellRadius=min(CellRadius1,CellRadius2)
According to the above-mentioned calculation method, the maximum cell radii supported by Format 0˜Format 4 are calculated respectively as shown in Table 1:
Supported cellFormatTCPTSEQTGTradiusFormat 0 3168Ts24576Ts  2976Ts14.5kmFormat 121024Ts 24576Ts15840Ts 77kmFormat 2 6240Ts 2*24576Ts 6048Ts30kmFormat 321024Ts2*24576Ts21984Ts 100kmFormat 4 448Ts 4096Ts 614Ts3km
In a limit situation, as to Format 3, when the Ncs is 839, the maximum range of the supported cell is 100 km. It can be found out that all of the five formats of the existing LTE PRACH cannot support the over-distance coverage beyond 100 km; while as to the over-distance coverage of the air line, it needs to support the coverage beyond 100 km and even 200 km.